Connections Between Adaptive Control and Optimization in Machine Learning

This paper demonstrates many immediate connections between adaptive control and optimization methods commonly employed in machine learning. Starting from common output error formulations, similarities in update law modifications are examined. Concepts in stability, performance, and learning, common to both fields are then discussed. Building on the similarities in update laws and common concepts, new intersections and opportunities for improved algorithm analysis are provided. In particular, a specific problem related to higher order learning is solved through insights obtained from these intersections.Comment: 18 page

A linear matrix inequality (LMI) approach to robust H2 sampled-data control for linear uncertain systems

In this paper, we consider the H2 sampled-data control for uncertain linear systems by the impulse response interpretation of the H2 norm. Two H2 measures for sampled-data systems are considered. The robust optimal control procedures subject to these two H2 criteria are proposed. The development is primarily concerned with a multirate treatment in which a periodic time-varying robust optimal control for uncertain linear systems is presented. To facilitate multirate control design, a new result of stability of hybrid system is established. Moreover, the single-rate case is also obtained as a special case. The sampling period is explicitly involved in the result which is superior to traditional methods. The solution procedures proposed in this paper are formulated as an optimization problem subject to linear matrix inequalities. Finally, we present a numerical example to demonstrate the proposed techniques.published_or_final_versio

Investigation of feedforward neural networks and its applications to some nonlinear control problems.

Ng Chi-fai.Thesis submitted in: December 2000.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 69-73).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiList of Figures --- p.viiiList of Tables --- p.ixChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation and Objectives --- p.1Chapter 1.2 --- Principles of Feedforward Neural Network Approximation --- p.1Chapter 1.3 --- Contribution of The Thesis --- p.5Chapter 1.4 --- Outline of The Thesis --- p.5Chapter 2 --- Feedforward Neural Networks: An Approximator for Nonlinear Control Law --- p.8Chapter 2.1 --- Optimization Methods Applied in Feedforward Neural Network Approximation --- p.8Chapter 2.2 --- Example in Supervised Learning --- p.10Chapter 2.2.1 --- Problem Description --- p.10Chapter 2.2.2 --- Neural Network Configuration and Training --- p.12Chapter 2.2.3 --- Simulation Result --- p.13Chapter 3 --- Neural Based Approximation of Center Manifold Equations --- p.19Chapter 3.1 --- Solving Center Manifold Equations by Feedforward Neural Network Approx- imation --- p.19Chapter 3.2 --- Example --- p.21Chapter 3.2.1 --- Problem Description --- p.21Chapter 3.2.2 --- Simulation Result --- p.24Chapter 3.2.3 --- Discussion --- p.24Chapter 4 --- Connection of Center Manifold Equations to Output Regulation Problem --- p.29Chapter 4.1 --- Output Regulation Theory --- p.29Chapter 4.2 --- Reduction of Regulator Equation into Center Manifold Equations --- p.31Chapter 5 --- Application to the Control Design of Ball and Beam System --- p.34Chapter 5.1 --- Problem Description --- p.34Chapter 5.2 --- Neural Approximation Solution of Center Manifold Equations --- p.37Chapter 5.3 --- Simulation Results --- p.38Chapter 5.4 --- Discussion --- p.45Chapter 6 --- Neural Based Disturbance Rejection of Nonlinear Benchmark Problem (TORA System) --- p.48Chapter 6.1 --- Problem Description --- p.48Chapter 6.2 --- Neural based Approximation of the Center Manifold Equations of TORA System --- p.51Chapter 6.3 --- Simulation Results --- p.53Chapter 6.4 --- Discussion --- p.59Chapter 7 --- Conclusion --- p.62Chapter 7.1 --- Future Works --- p.63Chapter A --- Center Manifold Theory --- p.64Chapter B --- Relation between Center Manifold Equation and Output Regulation Prob- lem --- p.66Biography --- p.68References --- p.6